Test: Arithmetical Reasoning - 2 - UPSC MCQ

# Test: Arithmetical Reasoning - 2 - UPSC MCQ

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## 15 Questions MCQ Test CSAT Preparation - Test: Arithmetical Reasoning - 2

Test: Arithmetical Reasoning - 2 for UPSC 2024 is part of CSAT Preparation preparation. The Test: Arithmetical Reasoning - 2 questions and answers have been prepared according to the UPSC exam syllabus.The Test: Arithmetical Reasoning - 2 MCQs are made for UPSC 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Arithmetical Reasoning - 2 below.
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Test: Arithmetical Reasoning - 2 - Question 1

### In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 1

Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x (4/3) = 24.
If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.
Therefore Number of girls in the class = (36 - 24) = 12.

Test: Arithmetical Reasoning - 2 - Question 2

### A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 2

Let son's age be x years. Then, father's age = (3x) years.
Five years ago, father's age = (3x - 5) years and son's age = (x - 5) years.
So, 3x - 5 = 4 (x - 5)  3x - 5 = 4x - 20  x = 15.

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Test: Arithmetical Reasoning - 2 - Question 3

### A waiter's salary consists of his salary and tips. During one week his tips were 5/4 of his salary. What fraction of his income came from tips?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 3

Test: Arithmetical Reasoning - 2 - Question 4

If you write down all the numbers from 1 to 100, then how many times do you write 3?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 4

Clearly, from 1 to 100, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
So, required number = 10 + 10 = 20.

Test: Arithmetical Reasoning - 2 - Question 5

If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 5

Test: Arithmetical Reasoning - 2 - Question 6

Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 6

L.C.M. of 6, 5, 7, 10 and 12 is 420.
So, the bells will toll together after every 420 seconds i.e. 7 minutes.
Now, 7 x 8 = 56 and 7 x 9 = 63.
Thus, in 1-hour (or 60 minutes), the bells will toll together 8 times, excluding the one at the start.

Test: Arithmetical Reasoning - 2 - Question 7

A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 10 men leave the bus and five women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 7

Originally, let number of women = x. Then, number of men = 2x.
So, in city Y, we have: (2x - 10) = (x + 5) or x - 15.
Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 45.

Test: Arithmetical Reasoning - 2 - Question 8

A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 8

Clearly, we have :

A = B - 3 ...(i)

D + 5 = E ...(ii)

A+C = 2E ...(iii)

B + D = A+C = 2E ...(iv)

A+B + C + D + E = 150 ...(v)

From (iii), (iv) and (v), we get: 5E = 150 or E = 30.

Putting E = 30 in (ii), we get: D = 25.

Putting E = 30 and D = 25 in (iv), we get: B = 35.

Putting B = 35 in (i), we get: A = 32.

Putting A = 32 and E = 30 in (iii), we get: C = 28.

Test: Arithmetical Reasoning - 2 - Question 9

A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 9

Since each pole at the corner of the plot is common to its two sides, so we have :

Total number of poles needed = 27 x 4 - 4 = 108 - 4 = 104.

Test: Arithmetical Reasoning - 2 - Question 10

In a city, 40% of the adults are illiterate while 85% of the children are literate. If the ratio of the adults to that of the children is 2 : 3, then what percent of the population is literate?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 10

Test: Arithmetical Reasoning - 2 - Question 11

A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 11

We have : A = 3B ...(i) and

C - 4 = 2 (A - 4) ...(ii)

Also, A + 4 = 31 or A= 31-4 = 27.

Putting A = 27 in (i), we get: B = 9.

Putting A = 27 in (ii), we get C = 50.

Test: Arithmetical Reasoning - 2 - Question 12

Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 12

Let Varan's age today = x years.

Then, Varan's age after 1 year = (x + 1) years.

Therefore x + 1 = 2 (x - 12)  x + 1 = 2x - 24  x = 25.

Test: Arithmetical Reasoning - 2 - Question 13

A bird shooter was askgd how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 13

There were all sparrows but six' means that six birds were not sparrows but only pigeons and ducks.

Similarly, number of sparrows + number of ducks = 6 and number of sparrows + number of pigeons = 6.

This is possible when there are 3 sparrows, 3 pigeons and 3 ducks i.e. 9 birds in all.

Test: Arithmetical Reasoning - 2 - Question 14

Mr. Johnson was to earn £ 300 and a free holiday for seven weeks' work. He worked for only 4 weeks and earned £ 30 and a free holiday. What was the value of the holiday?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 14

Test: Arithmetical Reasoning - 2 - Question 15

What is the smallest number of ducks that could swim in this formation - two ducks in front of a duck, two ducks behind a duck and a duck between two ducks?

Detailed Solution for Test: Arithmetical Reasoning - 2 - Question 15

Clearly, the smallest such number is 3.

Three ducks can be arranged as shown above to satisfy all the three given conditions.

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